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On the Derivation and the Properties of an Effective Hamiltonian for a Polaron in an External Magnetic Field
Author(s) -
Röseler J.,
Henneberger K.,
Fischbeck H. J.
Publication year - 1973
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220550215
Subject(s) - hamiltonian (control theory) , polaron , eigenvalues and eigenvectors , physics , magnetic field , mathematical physics , covariant hamiltonian field theory , quantum mechanics , quantum electrodynamics , hamiltonian system , mathematics , electron , mathematical optimization
The lowest eigenvalues of Frohlich's Hamiltonian with a magnetic field are approximately determined by solving the eigenvalue problem of an effective Hamiltonian for a polaron in a magnetic field. The effective Hamiltonian can be diagonalized without approximations, and the eigenvalue problem is reduced to the determination of the energy‐momentum relation of a free polaron. In the present paper it is shown in which manner the effective Hamiltonian can be derived from Frohlich's Hamiltonian with a magnetic field. The approximations being necessary for this derivation are justified on the condition ω c /ω 0 = |e| · | B |/ m c ω 0 ≪ 1 in the case of weak and intermediate coupling. Furthermore, the properties of the eigen‐value spectrum belonging to the effective Hamiltonian are discussed.